Step 1: The Background
The initial problem was this: the flashlight is supposed to take 3xAAA batteries. Harummph, I say. Completely useless. I bought it anyway, figuring I'd modify it to take a useful battery type.
Step 2: Battery carrier
Whipping out the calipers, I found the battery carrier to be 52mm in length and 22mm in diameter. So the idea was to find a rechargeable lithium battery that would fit within those dimensions.
Step 3: Lithium cells
One of the most common cells found in laptop batteries is the 18650 cell.
This means the cell is 18mm in diameter and 65.0mm in length.
Having a bunch of these, I tried to jam one in, but sadly it wouldn't fit. It was just too long.
So I went down to my local lithium battery super store, right down the street. Ermm, j/k. I went to the online electronic crap superstore based in Hong Kong. And I searched.
They had a 25500 lithium C cell, which was almost perfect. Well, just a tad too fat. I checked the internal diameter of the flashlight tube to be sure, and 22.5mm was the max it would accept.
After a few minutes it became apparent that the largest lithium battery that would fit is a 17340 cell. That would have left a horrible waste of space. I wasn't going to pay good money then wait 3 weeks for shipping time for that bad a solution.